Asian shares edged lower as investors fretted about slowing global growth with crude oil prices sinking on worries about weakening world demand and oversupply.
US crude futures dived 7 per cent the previous day, suffering their biggest one-day loss in more than three years. The contracts last stood at $55.72 per barrel following a descent to $54.75 overnight, their lowest since November 2017.
OPEC warned on Tuesday that a supply glut could emerge in 2019 as the world economy slows and rivals increase production more quickly than expected.
The concerns about global growth pushed MSCI's broadest index of Asia-Pacific shares outside Japan down 0.07 per cent.
Australian stocks fell 0.5 per cent, South Korea's KOSPI lost 0.2 per cent and Japan's Nikkei added 0.3 per cent.
The Dow and S&P 500 ended slightly lower on Tuesday as lower oil prices took a toll on energy shares, offsetting a small gain in technology stocks and renewed hopes for progress in US-China trade talks.
The Nasdaq managed to end essentially flat on Tuesday as a rebound in technology stocks kept the index out of negative territory.
Riskier assets have been under intense selling pressure over the past two months as worries about a peak in earnings growth added to international trade tensions and signs of slowing in global investment and growth.
"The markets would have reacted more positively to US-China trade and Brexit-related headlines a few months ago," said Makoto Noji, chief currency and foreign bond strategist at SMBC Nikko Securities in Tokyo.
"But currently there is more focus on the possibility of both the US and Chinese leaders maintaining their tough stance, with a compromise eluding them, and Brexit bogging down. Market sentiment is clearly cooling down."
The United Kingdom and European Union agreed on the text for a Brexit divorce deal on Tuesday. Prime Minister Theresa May will present the draft withdrawal agreement to her senior ministers on Wednesday for discussion and then decide on the next steps.
Lifted by the latest hopes for a Brexit deal, the pound extended overnight gains and was last 0.35 per cent higher at $1.3016.
Brexit hopes also supported the euro. The single currency was up 0.2 per cent at $1.1310 pulling back from a 17-month trough of $1.1216 brushed on Monday.
The euro's gains, however, were tempered by concerns over Italy's budget proposals. The European Commission rejected Italy's plan last month and has threatened to impose penalties if it is not revised to conform with EU regulations - something Rome has indicated it is unwilling to do.
The dollar index, which measures the greenback's strength against six major currencies, slipped overnight to 97.303.
The index had steadily climbed to a 16-month peak of 97.693 on Monday amid the ongoing US-China trade dispute and the Federal Reserve's commitment to keep gradually raising interest rates.
Also weighing on the dollar, US Treasury yields slid to more than one-week lows overnight as the sharp drop in oil prices suggested a more subdued inflation outlook.
US crude futures dived 7 per cent the previous day, suffering their biggest one-day loss in more than three years.